I was a LEO for 22 years and most of those on midnight shift. After dealing with drunks for so many years, my tolerance for being ariound them when I didn't have to be was very low. I doubt I would be able to play certain venues because of that.
If you are just entering, you are going to get stuck on afternoon shifts working Friday, Saturday and three weekdays; the shifts that anyone with seniority for the most part avoids.
Then as ACalbass points out, you may be asked to play in places that a cop may not be welcomed. As a cop you are expected (by many) to have a higher standard, and not associate with those people and that atmosphere. I had a sportbike and frequently rode with those "stunter" guys you see riding down the highway doing wheelies, I got a lot of crap from my segeant and chef when this was discovered.
So, yes you can still play but there will definitely be restrictions. And use common sense and don't play anywhere that can put your job at risk ie hardcore biker bars, strip joints, anyplace with any kind of drug trafficing...
If I want extended range, I whip out my six string!#179 at the Tricked Out Squier Club.